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Simplify this expression.
One of the benefits of leveling up in math is that you get to face more challenging skills.
But sometimes, those skills are really just old familiar skills in fancier clothes.
Just like when we added and subtracted rational expressions, all those numbers, variables,
and exponents don’t matter.
What you really have here are fractions, and strangely enough you can tackle them the same
way you would handle less scary-looking fractions.
With fractions, you just multiply together the numerators and denominators. You divide
them by multiplying the first fraction by the reciprocal of the second fraction. We’re
going to do the same thing with these rational expressions.
When we multiply two fractions together, we just multiply straight across.
When we multiply two rational expressions together, we still multiply straight across.
It just takes a few more steps.
When you multiply rational expressions, you are still allowed and encouraged to cross
cancel if you can, and you always simplify your answer if every single term has a common
factor.
When we divide rational expressions, we still multiply the first expression by the reciprocal
of the second expression.
Again, cross cancel where you can, and remember to simplify your answer.
Sometimes, you’ll have a quadratic or two thrown in. Just factor them. More often than
not, that will cause something to cancel out.
Now, what can we do with our original problem?
This is already a multiplication problem, so let’s cross cancel what we can.
Then, we’ll multiply what’s left.
This answer is already in simplest form, so we’re done.
Multiplying and dividing rational expressions is just like multiplying and dividing fractions.
Cross cancel if you can, and always simplify your answer.